I used telnet localhost 8080. Returned a "Could not open connection to the host on port 8080: Connection failed."

The company structure (as far as I know) is rather simple. Everything's connected to a server, which acts only as a file repository. Each laptop can be modified and used as the user pleases (within reason, of course). Kinda like how most multi-computer setups at home are. No domain login, or anything.

Was the root cause, that caused installation or instance to fail in the first place, fixed or even identified?

Before jumping away at trying to open a web app (Get Started), please re-verify the basic pieces.
I.e. is the instance running, with database opened? Does the listener have database services registered?

sqlplus / as sysdba

(exit from sqlplus)

lsnrctl stat

Please post result of above commands. Also verify that log files in config\log\ dir are free of errors.

You need a listener on port 8080 to know it needs to do something, and your machine needs to know 127.0.0.1 is localhost!

I had the same exact problem listed here, and went through all the steps, none of which solved the problem. I searched other forums for an answer as well. The guidance offered for setting the hosts file in
C:\Windows\System32\drivers\etc\hosts was incorrect. The line to add should be
127.0.0.1 localhost

NOT
127.0.0.1 localhost yourPCname or in Udo's example for Arnold
127.0.0.1 localhost arnold-PC

Once the host file was fixed, Get_Started worked without an issue.

I would also like to suggest restarting your machine after you perform the install even though the install said everything is running. Minimally after a restart, the %HTTPPORT% environment variable will be in affect at that point so you will no longer need to edit the properties of Get_Started. Check your services (Start > Control Panel > System and Security > Administrative Tools > Services ) and make sure the two Oracle services -- OracleServiceXE, OracleXETNSListener -- are started. Check any security agent running on your machine to make sure the agent is not preventing Oracle programs from running (Cisco Security Agent kept on shutting down these services) until I 'trusted' the untrusted program. Make sure your firewall allows the ports too!

orafad had it write when he noticed that 8080 was not listening. You should see
Listening Endpoints Summary...
(DESCRIPTION=(ADDRESS=(PROTOCOL=ipc)(PIPENAME=\\.\pipe\EXTPROC1ipc)))
(DESCRIPTION=(ADDRESS=(PROTOCOL=tcp)(HOST=_yourPCname_)(PORT=1521)))

The listener needs a valid hostname it its configuration, or a valid IPv4 address. If the host network setup is not quite correct, apex will also be not quite correct, and not exactly working. So take a look at the listener endpoints, in a command box:

lsnrctl status

...

endpoints...

...port=1521...

...port=8080...presentation=http ...

If the port=8080 entry is missing from the endpoints, the apex web pages will not work. Usually its caused by a less than 100% correct network configuration on the host.

One easy fix is stopping the listener and rename the listener.ora file, restart the listener, and try again.